Effects of localized μ-terms at the fixed points in magnetized orbifold models

We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called μ-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. It is known that, without such localized sources, the zero-mode degeneracy, which is identified as the generation in four-dimensional (4D) effective theories, is determined by the magnetic fluxes, and multi-Higgs models appear in general in magnetized orbifold models. We derive the analytic form of the μ-term matrix in the 4D effective theory, which is generated by the localized sources on T²/Z₂ orbifold fixed points, and find that the rank of the mass matrix for Higgs zero-modes is raised by the number of fixed points where nonvanishing μ-terms are located. We show some remarkable features of the mass eigenvalues and eigenstates, those are relevant to the low-energy phenomenology.